Curriculum Matters

When teachers and stake holders in education use the word curriculum, it’s important that this be properly defined.  District leaders and teachers may view curriculum as a pacing guide that describes the order in which content objectives are to be taught (Stein, Remillard, and Smith, 2007).  The view of curriculum may also be seen as the set of instruments that are used to instruct in which define in many ways how the content is taught (Stein, Remillard, and Smith, 2007).  Though standards and curriculum are interwoven, they are different.  Stein, Remillard, and Smith (2007) describe curriculum as “the substance or content of teaching and learning” (p. 321).  Standards may be taught through many different curriculums that encompass different methods or approaches to instruction, materials that are used, and order of instruction.

            Stein, Remillard, and Smith (2007) discussed differences between curriculum as the written curriculum, intended curriculum, and enacted curriculum.  The written curriculum is many times given to teachers through district leaders by pacing guides, texts, and pedagogical emphasis (Stein, Remillard, and Smith, 2007).  From this portion of curriculum develops through each teacher the intended curriculum that is found through planning what will actually take place in the classroom (Stein, Remillard, and Smith, 2007).  The actual implementation of the curriculum is described as the enacted curriculum (Stein, Remillard, and Smith, 2007).  Each of these components of curriculum plays critical roles in student learning, but also contributes to the difficulty of large scale studies effects on curriculum (Stein, Remillard, and Smith, 2007).

            One of the largest factors on how curriculum influences student learning is how teachers use them in the classroom (Stein, Remillard, and Smith, 2007).  This large variation is attributed to teachers picking and choosing what they want to use from the curriculum, not using the curriculum at all, completely using the curriculum, losing rigor encompassed in the curriculum, and teacher beliefs of the curriculum and how they should be used (Stein, Remillard, and Smith, 2007).  How teachers interact with the curriculum and its materials also create variation from classroom to classroom (Stein, Remillard, and Smith, 2007).   The rigor of curriculum cannot be fully understood unless teacher implementation, ability to implement, times for implementation, culture, support, and attitudes/beliefs are controlled (Stein, Remillard, and Smith, 2007).  Evidence from research also suggests the need for studies that attempt to control for these factors from researchers who are independent of the curriculum being enacted (Stein, Remillard, and Smith, 2007).

Assessments of curriculum materials have had mixed reviews over the years and has seen divergence largely from what are seen as goals of mathematics (Stein, Remillard, and Smith, 2007).  Reform based or standards based curriculum materials have focused more on problem solving, sense making, and the integration of content while conventional textbooks focus primarily on algorithms and student use of algorithms (Stein, Remillard, and Smith, 2007).  Assessment of standards based curriculum score higher than conventional textbooks when the goals of this curriculum are to develop meaning, relationship to real life mathematics, and present opportunities for student engagement in the Project 261 study and provide clear goals, appropriate for audience, engaging, motivational, appropriate assessment, ability to be used in multiple settings, relate to mathematical content standards, related to life, and increase student learning by the United States Department of Education (Stein, Remillard, and Smith, 2007).  These curriculum materials score lower in cases when the goals of curriculum are mastery of the mathematical core, procedural fluency, conceptual understanding, and ability to apply newly learned material into contextual situations as reported by Mathematically Correct (Stein, Remillard, and Smith, 2007).  Conventional textbook curriculum offers opportunities for students to master algorithms through repeated practice, thus if one believes math is best learned through direct instruction and skills practice conventional textbooks have benefits over standards based curriculum (Stein, Remillard, and Smith, 2007)

            Past research has largely focused on the ability of standards based curriculum to “keep up” with conventional counterpart curriculums in procedural skills and surpass them in conceptual knowledge and ability to solve non-routine problems (Stein, Remillard, and Smith, 2007).  Stein, Remillard, and Smith (2007) suggest however that students do best at tests that relate to how they were taught.  For these reasons, it is important for developers of Common Core State Standards assessments to create tests that measure not only content standards but practice standards.  If teachers are going to teach to a test, developers might as well make the test worthy to teach to.

            From this chapter, teachers should gather two major points.  First, good teaching is not what you teach, but how you teach.  What teachers foster inside their classroom through their enacted curriculum will describe what learning takes place (Stein, Remillard, and Smith, 2007).  Second, curriculums are developed in two large frameworks and are best used with specific goals in mind (Stein, Remillard, and Smith, 2007).  Standards based curriculums focus largely on students building knowledge with the guidance of the teacher while conventional curriculums lead the transfer, mediation, and creation of knowledge primarily to the teacher (Stein, Remillard, and Smith, 2007).  Both curriculums share the idea that mathematics should be understood and conceptualized by all, while they differ in their emphasis on procedural skills, standard integration, and emphasis on non-routine problems (Stein, Remillard, and Smith, 2007).  When teachers encourage learning by students, it is important for them to understand their overlying mathematical learning goals.

Stein, M.; Remillard, J. & Smith, M. (2007). How curriculum influences student learning. In F. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Charlotte: Information Age Publishing.

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